CN106845010A - Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony - Google Patents

Abstract

Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, it is included according to input signal and basic inequality principle the invention discloses a kind of, and constructing matrix line number and matrix columns in SDV algorithms has the Hankel matrixes of max product；According to input signal, its signal to noise ratio curve is drawn, and signal to noise ratio curve is analyzed, determine best available singular value order；The identification order in Prony algorithms is selected according to best available singular value order, establishes optimal identification order；Input signal is processed using the svd algorithm with Hankel matrixes and best available singular value order, obtains de-noising signal；De-noising signal is analyzed by the Prony algorithms with optimal identification order, recognizes low-frequency oscillation dominant pattern；The low-frequency oscillation dominant pattern discrimination method for being based on improving SVD noise reductions and Prony has noise inhibiting ability strong, the advantages of identification precision and the degree of accuracy high.

Description

Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony

Technical field

The present invention relates to field of power, and in particular to a kind of based on the low-frequency oscillation master for improving SVD noise reductions and Prony Waveguide mode discrimination method.

Background technology

The propulsion and power system scale interconnected with bulk power grid constantly expand, and are improving the reliability and warp of operation of power networks While Ji property, new potential safety hazard is also brought；Repeatedly there is the serious safety for having jeopardized power network of low-frequency oscillation in recent years Stable operation, causes the extensive concern of industrial quarters and academia；Therefore, Correct Analysis the Characteristics of Low Frequency Oscillations parameter is effectively suppression The important foundation of low-frequency oscillation of electric power system phenomenon processed.

Low Frequency Oscillation Analysis based on disturbed track directly can be analyzed to system output response, without detailed system Model and extensive characteristic value are calculated, and can adapt to the change of system operation mode and parameter, and system can be reflected in disturbance The influence of dynamic process and meter and various non-linear factors afterwards；It is Fourier transformation, small in the method for various signal analysis The application such as wave conversion widely, but is difficult to extract the attenuation coefficient of signal, that is, be difficult to obtain damping ratio this key character.

In recent years, Prony algorithms are widely used in Power System Analysis with control field, in power system In research, Prony analysis methods have wide applicability, particularly excellent in the System Discrimination in small-signal stability contorting field Gesture is fairly obvious；The information obtained using Prony analyses measured data is more accurate than the information that Perturbation Analysis are obtained, by right The Prony analyses of real system can directly obtain the information such as dominant characteristics root and its transmission function residual in system, with one most Excellent system order reduction model approaches former high-order model.

However, requirement of the Prony algorithms to input signal is higher, noise jamming can have a strong impact on Prony Pole formulas The precision of estimation, so that larger error occurs in the result for calculating；In the ideal case, the solution of Prony algorithms and uncomplicated, But under white noise background, the optimal solution of the complex random variables is a non-linear least square problem for difficulty, and SVD drops There are problems that being difficult to for Hankel matrixes exponent number and effective singular value order in making an uproar again.

The content of the invention

For above-mentioned deficiency of the prior art, the low-frequency oscillation based on improvement SVD noise reductions and Prony that the present invention is provided Dominant pattern discrimination method has noise inhibiting ability strong, the advantages of identification precision and the degree of accuracy high.

In order to reach foregoing invention purpose, the technical solution adopted by the present invention is：There is provided it is a kind of based on improve SVD noise reductions and The low-frequency oscillation dominant pattern discrimination method of Prony, it includes, according to input signal and basic inequality principle, constructing SDV Matrix line number and matrix columns have the Hankel matrixes of max product in algorithm；According to input signal, its signal to noise ratio is drawn bent Line, and signal to noise ratio curve is analyzed, determine best available singular value order；According to best available singular value order pair Identification order in Prony algorithms is selected, and establishes optimal identification order；Using with Hankel matrixes and best available strange The svd algorithm of different value order is processed input signal, obtains de-noising signal；By the Prony with optimal identification order Algorithm is analyzed to de-noising signal, recognizes low-frequency oscillation dominant pattern.

Further, S1 is concretely comprised the following steps：If Hankel matrixes line number is m, matrix columns is n, and input signal is X (N)={ x₁, x₂..., x_N, the signal points in input signal are N；According in inequality principle when m and n is equal or most connects Product both when near is maximum, establishes the value of matrix line number m and matrix columns n, and construct m × n ranks by phase space reconfiguration Hankel matrix Hs.

Further, the matrix line number m of Hankel matrix Hs is：

The matrix columns n of Hankel matrix Hs is：

N=N+1-m：

Wherein, N is the signal points in input signal；

Hankel matrix Hs are：

Wherein, N=m+n-1；D_m×nIt is the signal subspace without interference of making an uproar；W_m×nIt is noise signal subspace, { x₁, x₂..., x_NIt is input signal.

Further, S2 is concretely comprised the following steps：According to effective singular value order is different in SDV algorithms and obtains input signal Signal to noise ratio after noise reduction is different, draws out signal to noise ratio curve；And corresponding singular value when selecting that signal to noise ratio is maximum in input signal Order, as best available singular value order.

Further, best available singular value order is the optimal subset number of the middle fitting of optimal identification order.

Further, S4 is concretely comprised the following steps：Singular value decomposition is carried out to Hankel matrixes, the Hankel after being decomposed Matrix and its rank of matrix and singular value；Preceding K singular value is preserved, remaining singular value zero setting is recycled unusual The inverse process that value is decomposed obtains restructuring matrix, and restructuring matrix is carried out into inverse transformation according to the method for phase space reconfiguration, obtains noise reduction Signal；Wherein, the numerical value of K is equal to the numerical value of best available singular value order.

Further, the Hankel matrixes after decomposition are：

Wherein, m is matrix line number, and n is matrix columns, and U, V are orthogonal matrix, and ∑ is non-negative diagonal matrix, i.e.,：

Wherein, r is the order of Hankel matrix Hs, σ_iIt is the singular value of Hankel matrix Hs.

Further, S5 is concretely comprised the following steps：If low frequency oscillation mode is with any amplitude, phase, frequency and decay The linear combination of P exponential function of the factor, the functional form of its discrete time is：

Wherein, A_iIt is amplitude, θ_iIt is first phase, f_iIt is frequency, σ_iIt is decay factor, p_iIt is the number of the exponential function of fitting, N It is number of samples, Δ t is sampling time interval；WillAs the approximate of actual samples point y (n), cost function is built, and make The value of cost function is minimum, obtains discrete time function；According to discrete time function and the normal equation of Prony algorithms, led The amplitude of waveguide mode, phase, frequency and decay factor.

Further, the normal equation of Prony algorithms is：

Wherein,I, j=0,1 ..., p, x^*(n-i) be x (n-i) conjugation,P is the number of exponential function, a₁, a₂..., a_pIt is coefficient to be solved.

Discrete time function is：

Wherein,(n=0,1 ..., N-1),e(n) To define actual measured value y (n) and estimateError,b₁, b₂..., b_pTo wait to ask Solution coefficient.

Further, the amplitude of low-frequency oscillation dominant pattern, phase, frequency and decay factor are：

Wherein, Re is represented and is taken real part, and Im is represented and taken imaginary part, A_iIt is amplitude, θ_iIt is phase, f_iIt is frequency, σ_iFor decay because Son.

Beneficial effects of the present invention are：This is based on improving the low-frequency oscillation dominant pattern discrimination method of SVD noise reductions and Prony Optimal Hankel matrixes order is determined using basic inequality and proposes to solve singular value order select permeability using signal to noise ratio, Data are pre-processed using SVD noise-removed technologies are improved, improves the signal to noise ratio of signal, reduced noise and Prony is analyzed The influence of result；And leading shaking of the algorithm is further demonstrated by Simulation Example having that noise inhibiting ability is strong, pick out The advantages of swinging pattern high precision, being capable of accurate Identification of Power System low-frequency oscillation dominant pattern.

Brief description of the drawings

Fig. 1 gives the oscillator signal in MATLAB environment and adds the oscillogram after making an uproar.

Fig. 2 show schematically after carrying out singular value decomposition to Hankel matrixes, retains singular value order and is respectively 1, 2...10 signal to noise ratio curve map.

Fig. 3 show schematically in MATLAB environment curve and original signal curve map after oscillator signal noise reduction.

Fig. 4 show schematically the matched curve figure of Prony38 ranks.

Fig. 5 show schematically the 6 rank optimal subset matched curve figures of Prony.

Fig. 6 show schematically 6 ranks fitting square error curve figure.

Fig. 7 show schematically the schematic diagram of power-angle curve.

Fig. 8 show schematically after carrying out singular value decomposition to power-angle curve, retains singular value order and is respectively 1, 2 ..., 12 signal to noise ratio curve map.

Fig. 9 show schematically the comparison diagram of the noise reduction curve and original signal curve in the node system of WSCC3 machines 9.

Figure 10 show schematically the matched curve figure of Prony50 ranks.

Figure 11 show schematically the 7 rank optimal subset matched curve figures of Prony.

Figure 12 show schematically 7 ranks fitting square error curve figure.

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation is described, it is clear that described embodiment is only an embodiment of the present invention, rather than whole embodiments.Based on this Embodiment in invention, the every other reality that those of ordinary skill in the art are obtained under the premise of creative work is not made Example is applied, protection scope of the present invention is belonged to.

For the sake of simplicity, herein below eliminates the common technical knowledge well known to technical field technical staff.

This is based on improvement SVD noise reductions and the low-frequency oscillation dominant pattern discrimination method of Prony includes：

S1, according to input signal and basic inequality principle, constructing matrix line number and matrix columns in SDV algorithms has The Hankel matrixes of max product；In specific implementation, for same signal, different structure can be reconstructed Hankel matrixes, the SVD separating resultings without that can make signal between isostructural Hankel matrixes produce very big difference, direct shadow Ring the noise reduction of signal；In order to realize being sufficiently separated for signal and noise, because constructing the line number and columns of Hankel matrixes Product is maximum as far as possible.

In practical operation, if Hankel matrixes line number is m, matrix columns is n, and input signal is X (N)={ x₁, x₂..., x_N, the signal points in input signal are N；According in inequality principle when m and n is equal or closest to when both Product is maximum, establishes the value of matrix line number m and matrix columns n, and then ensures that signal and noise can obtain sufficiently separation, and leads to Cross the Hankel matrix Hs that phase space reconfiguration constructs m × n ranks.

The product maximum for meeting Hankel matrix line number m and Hankel matrix columns ns depends primarily on the strange of signal points N Idol；In specific implementation, the parity of binding signal points N determines Hankel matrix line number m and columns n, i.e. Hankel squares Battle array H matrix line number m be：

The matrix columns n of Hankel matrix Hs is：

N=N+1-m；

Wherein, N is the signal points in input signal；After Hankel matrix line number m and columns n is determined, pass through Phase space reconfiguration constructs the Hankel matrix Hs of m × n ranks, and the Hankel matrix Hs of construction are：

Wherein, N=m+n-1；D_m×nIt is the signal subspace without interference of making an uproar；W_m×nIt is noise signal subspace, { x₁, x₂..., x_NIt is input signal.

S2, according to input signal, draw its signal to noise ratio curve, and signal to noise ratio curve is analyzed, determine best available Singular value order；It is different and after obtaining input signal noise reduction according to effective singular value order in SDV algorithms in specific implementation Signal to noise ratio is different, draws out signal to noise ratio curve；And corresponding singular value order when selecting that signal to noise ratio is maximum in input signal, as Best available singular value order；It efficiently solves singular value threshold value in the prior art and is difficult to the problem for determining；It selects letter The signal reconstruction made an uproar during than highest, can reach signal to noise ratio highest and noise reduction is most obvious, and then reduce noise to Prony points Analyse the influence of result.

S3, the identification order in Prony algorithms is selected according to best available singular value order, establish optimal identification Order；It determines according to the order that best available singular value order carries out Prony identifications, efficiently solves Prony and recognize rank The difficulty of secondary selection；In specific implementation, the definition of signal to noise ratio is：

SNR=10log₁₀(P_s/P_n)；

Wherein, P_sIt is original signal energy, P_nNoise energy；And best available singular value order is optimal identification order The optimal subset number of middle fitting.

S4, input signal is processed using the svd algorithm with Hankel matrixes and best available singular value order, Obtain de-noising signal；In specific implementation, singular value decomposition is carried out to Hankel matrixes, the Hankel matrixes after being decomposed and Its rank of matrix and singular value；Preceding K singular value is preserved, by remaining singular value zero setting, singular value decomposition is recycled Inverse process obtain restructuring matrix, restructuring matrix is carried out into inverse transformation according to the method for phase space reconfiguration, obtain de-noising signal；Its In, the numerical value of K is equal to the numerical value of best available singular value order, and the Hankel matrixes after decomposition are：

Wherein, m is matrix line number, and n is matrix columns, and U, V are orthogonal matrix, and ∑ is non-negative diagonal matrix, i.e.,：

Wherein, r is the order of Hankel matrix Hs, σ_iIt is the singular value of Hankel matrix Hs.

S5, de-noising signal is analyzed by the Prony algorithms with optimal identification order, identification low-frequency oscillation is dominated Pattern；In specific implementation, Prony algorithms are the algorithms most in use for extracting Stationary Oscillation pattern, and it is directed to equidistant sampled point；If Low frequency oscillation mode is the linear combination of the P exponential function with any amplitude, phase, frequency and decay factor, and its is discrete The functional form of time is：

Wherein, A_iIt is amplitude, θ_iIt is first phase, f_iIt is frequency, σ_iIt is decay factor, p_iIt is the number of the exponential function of fitting, N It is number of samples, Δ t is sampling time interval；WillAs the approximate of actual samples point y (n), cost function is built, and make The value of cost function is minimum, obtains discrete time function；According to discrete time function and the normal equation of Prony algorithms, led The amplitude of waveguide mode, phase, frequency and decay factor.

In practical operation, willUsed as the approximate of actual samples point y (n), the method for its parameter identification is construction cost Function of ε, orderTo make ε reach minimum, so as to obtainIn each parameter, this demand solution is non-linear Equation group, is changed by a series of mathematics of the prior art, can release difierence equation as follows：

In order to set up Prony algorithms, actual measured value y (n) and estimate are definedError be e (n), i.e.,WillBring into difierence equation, and then obtain equation (n=o, 1 ..., N-1)；Wherein,

So if object function is changed to so thatMinimum, then can find one group of linear equation：

To make object functionIt is minimum value, orderThen have Wherein, x^*(n-i) be x (n-i) conjugation；Now, defineI, j=0,1 ..., p, i.e., The normal equation that can obtain Prony algorithms is：

Wherein,I, j=0,1 ..., p, x^*(n-i) be x (n-i) conjugation,P is the number of exponential function, a₁, a₂..., a_pIt is coefficient to be solved；Can be Number a₁, a₂..., a_p, further solve proper polynomial 1+a₁z^-1+...+a_pz^-p=0 obtain characteristic root Zi, i=1,2 ..., P, and enable its simplification(n=1,2 ..., N-1), can obtain discrete time function, its Discrete time function is：

Wherein,(n=0,1 ..., N-1),For Define actual measured value y (n) and estimateError,B1, b2 ..., b_pFor to be solved Coefficient；Finally the normal equation to discrete time function and Prony algorithms is solved, and can calculate shaking for low-frequency oscillation dominant pattern Width, phase, frequency and decay factor, and then establish the dominant pattern of low-frequency oscillation；In specific implementation, its low-frequency oscillation is dominated The amplitude of pattern, phase, frequency and decay factor are：

Wherein, Re is represented and is taken real part, and Im is represented and taken imaginary part, A_iIt is amplitude, θ_iIt is phase, f_iIt is frequency, σ_iFor decay because Son.

This is carried out unusual based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony according to signal to noise ratio It is worth the selection of effective order, SVD is solved well and is chosen on threshold value in reconstructed reduced noise does not cause just noise reduction to be failed to understand Aobvious problem；Determine the selection of Prony orders according to the best available singular value orders of SVD, it is to avoid the selection of Prony orders is not When the problem for causing identification result error big；And improved SVD noise reductions are substantially, improve the signal to noise ratio of signal, reduce Influence of the noise to Prony analysis results.

In practical operation, in order to verify the low-frequency oscillation master based on improvement SVD noise reductions and Prony proposed by the invention The validity of waveguide mode discrimination method, simulating, verifying is carried out by Matlab/Simulink emulation platforms to it.

In specific implementation, one group of waveform of oscillator signal is produced in MATLAB environment, if this group of ripple of oscillator signal Shape is：

As shown in figure 1, Fig. 1 gives the oscillogram added after making an uproar；Wherein, sample frequency is taken for 1kHz, observation window length It is 5s, is 0 to average is added in X signal, variance is 1 white Gaussian noise, the waveform after obtaining plus making an uproar.

As shown in Fig. 2 Fig. 2 show schematically after carrying out singular value decomposition to Hankel matrixes, retain singular value rank The secondary signal to noise ratio curve map for being respectively 1,2...10；By the signal to noise ratio curve map understand when retain singular value number be 6 when Wait, the Signal-to-Noise highest after noise reduction is best suitable for for carrying out Prony analyses；Now, choose and retain best available singular value Order is 6, and carries out signal reconstruction noise reduction.

As shown in figure 3, Fig. 3 show schematically curve and original signal curve map after noise reduction, by curve after noise reduction and original Signal curve can be seen that the curve for fitting has good precision, and noise reduction substantially, is suitable for Prony analyses.

As shown in figure 4, Fig. 4 show schematically the matched curve figure of Prony38 ranks, wherein, matched curve and noise reduction Curve coincide substantially afterwards, and identification precision is high；The precision of Prony identifications will be influenceed when sampled data is overstocked, therefore by after noise reduction Signal enter the sampling of between-line spacing 30, new sequence is the step-length of 0.03s, and total duration is 5s, and new sequence is carried out into the ranks of Prony 38 Fitting.

As shown in Figure 5 and Figure 6, Fig. 5 show schematically the 6 rank optimal subset matched curve figures of Prony, and Fig. 6 illustrates Property give 6 ranks fitting square error curve figure；It is 6 according to the best available singular value order retained in SDV algorithms, 6 rank optimal subsets are chosen in the fitting of the ranks of Prony 38 to be fitted, its fitting precision is high；So determining singular value using signal to noise ratio While order is reconstructed, the difficult problem that Prony determines rank is also solved, its fitting difference of two squares is less than 0.01, meets Prony Fitting precision requirement.

Ideal value, SVD+Prony and tradition Prony are contrasting as shown in the table of both frequency and damping：

As can be seen from the above table, improvement SVD noise reductions proposed by the present invention and Prony and traditional Prony are in frequency and resistance Contrast of both Buddhist nun, is being similarly the fitting of 38 ranks, and in the case that 6 rank optimal subsets of selection are fitted, traditional Prony can only Frequency and the damping of exit pattern 2 are recognized, damping and the frequency of exit pattern 3 can not be recognized, the frequency and damping for pattern 1 are distinguished Know error and reach more than 60%, and 3 patterns can be good when being recognized using improved SVD noise reductions and Prony algorithms Recognized, be particularly less than 2.5% in frequency estimation error, damping Identification Errors are less than 4%, it can be seen that improved SVD Noise reduction and Pronyy algorithms can be very good to recognize noise signal.

In practical operation, example is made at Based on Power System Analysis Software Package (PSASP) from the node system of WSCC3 machines 9 In carry out simulation analysis, system generator total capacity is 567.5MW, and burden with power is 315MW, and generator is using 3 rank E ' q changes Model, excitation system chooses 1 type excitation system in PSASP, and load uses constant-impedance load.

SVD and Prony Algorithm Analysis is improved to power-angle curve, it is small dry in the identification result that will be obtained and PSASP Disturb the system dominant mode that stability analysis obtains to be contrasted, checking SVD and Prony algorithms having in terms of noise signal is processed Good precision.

In view of high-frequency noise is contained in practical measurement signals, actual signal, checking are reproduced in order to more real The validity that method proposed by the present invention is recognized to live actual signal, to there is the generator rotor angle ripple after Sudden Three-phase Short Circuit in example Shape adds higher hamonic wave and white noise, makes the curve that it is obtained closer to live practical measurement signals.

As shown in Figure 7 and Figure 8, Fig. 7 show schematically the schematic diagram of power-angle curve, and Fig. 8 show schematically right After power-angle curve carries out singular value decomposition, retain the signal to noise ratio curve map that singular value order is respectively 1,2 ..., 12；By noise Be can be seen that when effective singular value order retains 7 than curve, signal to noise ratio highest, choosing the best available singular value order of reservation is 7。

As shown in figure 9, Fig. 9 show schematically the comparison diagram of noise reduction curve and original signal curve, it can be seen that fit Curve there is good precision, noise reduction substantially, is suitable for Prony analyses.

As shown in Figure 10 and Figure 11, Figure 10 show schematically the matched curve figure of Prony50 ranks, and Figure 11 is schematical Give the 7 rank optimal subset matched curve figures of Prony；Curve after noise reduction is carried out into Prony50 rank fittings, matched curve with Curve coincide substantially after noise reduction, and identification precision is high；The singular value number retained according to SVD is 7, then be fitted in the ranks of Prony 50 7 rank optimal subsets of middle selection are fitted, and fitting precision is high, can be good at picking out the control oscillation modes in system.

As shown in figure 12, Figure 12 show schematically 7 ranks fitting square error curve figure, it can be seen that the fitting difference of two squares Less than 0.01, meet Prony fitting precision requirements.

Ideal value, SVD+Prony and tradition Prony are contrasting as shown in the table of both frequency and damping：

The fitting of 50 ranks is being similarly, in the case that 7 rank optimal subsets of selection are fitted, traditional Prony is damped in identification Aspect error reaches more than 38%, and when being recognized using improved SVD noise reductions and Prony algorithms, to system in 2 masters Leading oscillation mode can be recognized well, particularly be below 1.7% in frequency estimation error, and damping Identification Errors are less than 9%, the identification precision of more traditional Prony is greatly improved, so the improved SVD noise reductions and Prony of present invention use are calculated Method can be very good to recognize noise signal.

In specific implementation, the node Simulation Example of above-mentioned 3 machine 9 demonstrates the algorithm has that noise inhibiting ability is strong, identification The advantages of control oscillation modes high precision for going out, being capable of accurate Identification of Power System low-frequency oscillation dominant pattern.

This is based on improving SVD noise reductions and the low-frequency oscillation dominant pattern discrimination method of Prony is determined using basic inequality Optimal Hankel matrixes order simultaneously proposes to solve singular value order select permeability using signal to noise ratio, using improving SVD denoising skills Art is pre-processed to data, improves the signal to noise ratio of signal, reduces influence of the noise to Prony analysis results；And enter one Walk and demonstrate the algorithm by Simulation Example to have noise inhibiting ability is strong, pick out control oscillation modes precision high etc. excellent Point, being capable of accurate Identification of Power System low-frequency oscillation dominant pattern.

The foregoing description of the disclosed embodiments, enables professional and technical personnel in the field to realize or uses the present invention. Various modifications to these embodiments will make it will be apparent that defined herein one for those skilled in the art As principle can in other embodiments be realized in the case of the spirit or scope for not departing from invention.Therefore, the present invention will not Can be limited and the embodiments shown herein, and be to fit to consistent with principles disclosed herein and novel features Scope most wide.

Claims (10)

1. a kind of based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, it is characterised in that including：

S1, according to input signal and basic inequality principle, constructing matrix line number and matrix columns in SDV algorithms has maximum The Hankel matrixes of product；

S2, according to the input signal, its signal to noise ratio curve is drawn, and the signal to noise ratio curve is analyzed, it is determined that most preferably Effective singular value order；

S3, the identification order in Prony algorithms is selected according to the best available singular value order, establish optimal identification Order；

S4, input signal is processed using the svd algorithm with the Hankel matrixes and best available singular value order, Obtain de-noising signal；

S5, de-noising signal is analyzed by the Prony algorithms with optimal identification order, the leading mould of identification low-frequency oscillation Formula.

2. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by, the S1's concretely comprises the following steps：If Hankel matrixes line number be m, matrix columns be n, input signal be X (N)= {x₁, x₂..., x_N, the signal points in input signal are N；According in inequality principle when m and n is equal or closest to when two The product of person is maximum, establishes the value of matrix line number m and matrix columns n, and the Hankel of m × n ranks is constructed by phase space reconfiguration Matrix H.

3. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by：The matrix line number m of the Hankel matrix Hs is：

The matrix columns n of the Hankel matrix Hs is：N=N+1-m；Wherein, N is the signal points in input signal；

The Hankel matrix Hs are：

$H_{m\×n}=\left(\begin{array}{cccc}{x}_1& x_2& \mathrm{...}& x_n\\ x_2& x_3& \mathrm{...}& x_{n+1}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ x_m& x_{m+1}& \mathrm{...}& x_N\end{array}\right)=D_{m\×n}+W_{m\×n};$

Wherein, N=m+n-1；D_m×nIt is the signal subspace without interference of making an uproar；W_m×nIt is noise signal subspace, { x₁, x₂..., x_NIt is input signal.

4. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by, the S2's concretely comprises the following steps：

It is different different with the signal to noise ratio after input signal noise reduction is obtained according to effective singular value order in SDV algorithms, draw out letter Make an uproar and compare curve；And corresponding singular value order, as best available singular value order when selecting that signal to noise ratio is maximum in input signal.

5. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by：The best available singular value order is the optimal subset number being fitted in optimal identification order.

6. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by, the S4's concretely comprises the following steps：Singular value decomposition is carried out to the Hankel matrixes, the Hankel after being decomposed Matrix and its rank of matrix and singular value；Preceding K singular value is preserved, remaining singular value zero setting is recycled unusual The inverse process that value is decomposed obtains restructuring matrix, and restructuring matrix is carried out into inverse transformation according to the method for phase space reconfiguration, obtains noise reduction Signal；Wherein, the numerical value of K is equal to the numerical value of best available singular value order.

7. according to claim 6 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by：Hankel matrixes after the decomposition are：

$H_{m\×n}=U_{m\×m}{\Σ}_{m\×n}{V}_{n\×n}^T;$

Wherein, m is matrix line number, and n is matrix columns, and U, V are orthogonal matrix, and ∑ is non-negative diagonal matrix, i.e.,：

$\left\{\begin{array}{c}\mathrm{\Σ}=\left(\begin{array}{cc}S& 0\\ 0& 0\end{array}\right),S=diag({\mathrm{\σ}}_1,{\mathrm{\σ}}_2,...,{\mathrm{\σ}}_r)\\ {\mathrm{\σ}}_i=\mathrm{\Σ}(i,i),{\mathrm{\σ}}_{i-1}\≥{\mathrm{\σ}}_i,i=1,2,...,{\mathrm{\σ}}_r\end{array}\right.;$

Wherein, r is the order of Hankel matrix Hs, σ_iIt is the singular value of Hankel matrix Hs.

8. according to claim 1 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by, the S5's concretely comprises the following steps：If low frequency oscillation mode is with any amplitude, phase, frequency and decay factor P exponential function linear combination, the functional form of its discrete time is：

$\hat{y}\left(n\right)=\underset{i=1}{\overset{p}{\Σ}}{b}_i{z}_i^n=\underset{i=1}{\overset{p}{\Σ}}{A}_i{e}^{{\mathrm{j\θ}}_i}{e}^{({\mathrm{\σ}}_i+j2{\mathrm{\πf}}_i)\mathrm{\Δ}t},(n=1,2,...,N-1);$

Wherein, A_iIt is amplitude, θ_iIt is first phase, f_iIt is frequency, σ_iIt is decay factor, p_iIt is the number of the exponential function of fitting, N is to adopt Sample number, Δ t is sampling time interval；WillAs the approximate of actual samples point y (n), cost function is built, and make cost The value of function is minimum, obtains discrete time function；According to the discrete time function and the normal equation of Prony algorithms, led The amplitude of waveguide mode, phase, frequency and decay factor.

9. according to claim 8 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by：The normal equation of the Prony algorithms is：

$\left[\begin{array}{cccc}r(0,0)& r(0,1)& \mathrm{...}& r(0,p)\\ r(1,0)& r(1,1)& \mathrm{...}& r(1,p)\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ r(p,0)& r(p,1)& \mathrm{...}& r(p,p)\end{array}\right]\left[\begin{array}{c}1\\ a_1\\ \mathrm{...}\\ a_p\end{array}\right]=\left[\begin{array}{c}{\mathrm{\ϵ}}_p\\ 0\\ \mathrm{...}\\ 0\end{array}\right];$

Wherein,x^*(n-i) be x (n-i) conjugation,P is the number of exponential function, a₁, a₂..., a_pIt is coefficient to be solved；

The discrete time function is：

$\left[\begin{array}{cccc}1& 2& ...& 1\\ z_1& z_2& ...& z_p\\ ...& ...& ...& ...\\ z_1^{N-1}& z_2^{N-1}& ...& z_p^{N-1}\end{array}\right]\left[\begin{array}{c}{b}_1\\ b_2\\ ...\\ b_p\end{array}\right]=\left[\begin{array}{c}y\left(1\right)\\ y\left(2\right)\\ ...\\ y\left(N\right)\end{array}\right];$

Wherein,e(n) To define actual measured value y (n) and estimateError,b₁, b₂..., b_pTo wait to ask Solution coefficient.

10. according to claim 9 based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony, its It is characterised by：The amplitude of the low-frequency oscillation dominant pattern, phase, frequency and decay factor are：

$\left\{\begin{array}{c}{A}_i=\left|b_i\right|,{\mathrm{\θ}}_i=arctan\frac{\mathrm{Im}\left(b_i\right)}{\mathrm{Re}\left(b_i\right)}\\ {\mathrm{\σ}}_i=\frac{ln\left(z_i\right)}{\mathrm{\Δ}t},f_i=\frac{1}{2\mathrm{\π}\mathrm{\Δ}t}arctan\frac{\mathrm{Im}\left(z_i\right)}{\mathrm{Re}\left(z_i\right)}\end{array}\right.;$

Wherein, Re is represented and is taken real part, and Im is represented and taken imaginary part, A_iIt is amplitude, θ_iIt is phase, f_iIt is frequency, σ_iIt is decay factor.